Question: Simplify. Remove all perfect squares from inside the square root. Assume $z$ is positive. $\sqrt{72z^5}=$
Answer: Factor $72$ and find the greatest perfect square: $72=2\cdot 2\cdot 3\cdot 3\cdot 2=6^2\cdot 2$ Find the greatest perfect square in $z^5$ : $z^5=\left(z^2\right)^2\cdot z$ $\begin{aligned} \sqrt{72z^5}&=\sqrt{6^2\cdot 2\cdot \left(z^2\right)^2\cdot z} \\\\ &=\sqrt{6^2}\cdot \sqrt{2} \cdot \sqrt{\left(z^2\right)^2}\cdot \sqrt{z} \\\\ &=6\cdot \sqrt{2} \cdot z^2\cdot \sqrt{z} \\\\ &=6z^2\sqrt{2z} \end{aligned}$